The instructions for upgrading the JDK to 6 for 11i are contained in the following note:
Using J2SE Version 6 with Oracle E-Business Suite 11i (Doc ID 401561.1)
I do not recommend installing the .bin version as that goes only to a directory in the root filesystem. I prefer to install the .tar.gz file which you can extract anywhere. If you install the .tar.gz file into $COMMON_TOP, the upgraded JDK will at least come along with a clone, rather than be tied to the OS of the source.
Thanks for the update, as per the note 2241334.1 mentions below patches to be applied but we are at JDK 6u45 and in the note 1439822.1 JDK 6 update 151 patch is 25474980 and after the download it extracts jdk-6u151-linux-i586.bin and jdk-6u151-linux-i586-rpm.bin
Oracle JRE 6 Update 151 Patch 25474983
Oracle JDK 6 Update 151 Patch 25474980
It is confusing a lot.
Try to install jdk-6u151-linux-i586.bin and see if it installs into a directory you choose. I am sure the rpm will install into a default OS directory.
Also be advised, I am not 100% sure the very latest versions of 1.6 JDK play nicely with EBS. The last time I tried this I could not even start the applications, and reverted back to 1.6.0_30.